Best Known (103, 103+29, s)-Nets in Base 4
(103, 103+29, 1044)-Net over F4 — Constructive and digital
Digital (103, 132, 1044)-net over F4, using
- trace code for nets [i] based on digital (4, 33, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
(103, 103+29, 3016)-Net over F4 — Digital
Digital (103, 132, 3016)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4132, 3016, F4, 29) (dual of [3016, 2884, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4132, 4119, F4, 29) (dual of [4119, 3987, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 23, F4, 3) (dual of [23, 18, 4]-code or 23-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4132, 4119, F4, 29) (dual of [4119, 3987, 30]-code), using
(103, 103+29, 866746)-Net in Base 4 — Upper bound on s
There is no (103, 132, 866747)-net in base 4, because
- 1 times m-reduction [i] would yield (103, 131, 866747)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7 410720 022441 012409 868653 912082 305183 219250 611921 687417 919775 362665 701391 386204 > 4131 [i]